Baked normals Look a Strange
A likely scenario would be if the normals were inverted. That happens for example if the geometry is inverted(scaled by negative values) at some point during modeling to mirror it. You should go to edit mode (tab), select everything (a) and recalculate normals before baking them. The hotkey is ctrl+n in 2.79 and shift+n in 2.80. You can access functions related to normals in the ctrl+f or Mesh > Faces and Mesh>Normals menus in 2.79, while in 2.80 there is a dedicated Normals menu alt+n. 

However in this particual case the issue is the normal map made with overlaping UVs for symetrical geometry. If you have a look at a normal map of a symetrical object, the normals are not mirrored - they differ on each side so if you mirror them you get an incorrect result.